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Whether or not your father's remaining property is part of the HOA or not is a very "cut and dry" question - Common Interest Developments (such as HOAs, Condo Associations, etc.) are made up of "reciprocal easements" between each of the properties that are members of the Association. You will find these easement restrictions in the recorded title documents for the properties themselves (so there will be something in the publicly recorded records at the County Recorder's Office showing whether or not your father's property is part of the HOA (and therefore whether or not it is obligated to pay HOA assessments).
I recommend retaining a title company to run the search on the property - they will do the search of the public records for you much more thoroughly than you will trying to navigate these documents yourself (you don't want to miss or overlook something, and they don't charge very much for a simple title search).
Regarding access to the property, this gets much more complicated. If there is no access to the lot you may be able to argue for an "easement by necessity" to the property, this is a very rare type of easement granted to properties that are truly "landlocked" (have no other means of ingress or egress), but you may end up having to retain a lawyer for this type of thing - I assume the developer isn't willing to work with you on this.
Alternatively, the title search (above) may show that you actually already have an easement (your father may have negotiated for one to remain on his property), and therefore you can simply enforce that easement against the developer - demand access to your property.